A Modern View on Merton's Jump-Diffusion Model

Gerald Cheang and Carl Chiarella
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Gerald Cheang: Centre for Industrial and Applied Mathematics, School of Mathematics and Statistics, University of South Australia

No 287, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: Merton has provided a formula for the price of a European call option on a single stock where the stock price process contains a continuous Poisson jump component, in addition to a continuous log-normally distributed component. In Merton's analysis, the jump-risk is not priced. Thus the distribution of the jump-arrivals and the jump-sizes do not change under the change of measure. We go onto introduce a Radon-Nikodym derivative process that induces the change of measure from the market measure to an equivalent martingale measure. The choice of parameters in the Radon-Nikodym derivative allows us to price the option under different financial-economic scenarios. We introduce a hedging argument that eliminates the jump-risk in some sort of averaged sense, and derive an integro-partial differential equation of the option price that is related to the one obtained by Merton.

Keywords: financial derivatives; compound Poisson processes; equivalent martingale measure; hedging portfolio (search for similar items in EconPapers)
Pages: 14 pages
Date: 2011-01-01
New Economics Papers: this item is included in nep-rmg
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Citations: View citations in EconPapers (6)

Published as: Cheang, G. and Chiarella, C., 2012, "A Modern View on Merton's Jump-Diffusion Model", In: Advances in Statistics, Probability and Actuarial Science: Stochastic Processes, Finance and Control, 217-234.

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